Nadal was given the benefit of a walkover in the second round after the withdrawal of Thanasi Kokkinakis and, in truth, he was never really tested by Chung on Arthur Ashe Stadium.
The three-time champion was in complete control throughout, his win setting up a last-16 clash with Marin Cilic or John Isner.
Chung had come from two sets down to beat Nadal's compatriot Fernando Verdasco in the previous round, but there were never any signs of such heroics being repeated once Nadal forged ahead.
The Korean qualifier produced only flashes of the brilliance that saw him reach the Australian Open semi-finals in 2018, and tougher tests are sure to await Nadal as he bids to regain the trophy he previously won in 2017.
Nadal struck the opening blow in the sixth game of the match as Chung sent a cross-court backhand wide.
Chung actually hit five aces to Nadal's four, but it was one off the Spaniard's racquet that wrapped up the first set.
A scintillating forehand down the line provided Nadal with what proved the decisive break in the second set and he did not have to wait long to make inroads in the third.
The third game of the set saw Chung drag a forehand off-target as he faded badly against the physical challenge presented by Nadal, the 23-year-old having only returned from injury at the end of July.
Asked about the potential benefit of a comfortable opening week in which he has only had to play two matches, Nadal said: "You never know, last year I had some tough matches and then in the semi-finals I had to retire [against Juan Martin Del Potro].
"You never know what's better. I have a tough opponent, John Isner or Marin Cilic [in the fourth round], I need to be ready for this, I can't think further than this."